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Schrodingers Equation

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that the function [tex]\Psi(x,t)=Asin(kx- \omega t)[/tex] does not satisfy the time-independent Schrodinger Equation.

    2. Relevant equations
    Time independet SE

    3. The attempt at a solution
    I think i have to solve for derivative of [tex]\Psi(x,t)/t[/tex] and second derivative of [tex]\Psi(x,t)/x[/tex] but i'm not sure how to answer the question.

    I attempted to differentiate the wave function with respect to time and space so that i got
    [tex]\partial\Psi(x,t)/\partial t = -\omega Acos(kx-\omegat)[/tex]
    and that [tex]\partial^2\Psi(x,t)/\partial x^x = -kAsin(kx-\omegat)[/tex]

    If so, how do i prove that the original function does not satisfy the TDSE?
    Last edited: Mar 25, 2009
  2. jcsd
  3. Mar 25, 2009 #2
    The time-independent Schrödinger equation says Hψ = Eψ, where E is the eigenvalue. The Hamiltonian will tell you what to differentiate with respect to.
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